A task that the servers allocated to your host - but effectively never arrived, or never finished arriving - perhaps due to network congestion. When your host reports, it tells the servers what it has in its cache - if that doesn't agree with what the server thinks you have, the servers resend any tasks your host hasn't got but should have. These lost tasks are often called ghosts.
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What I don't understand about lost tasks is why they are only resent in batches of 20.

Because that is the arbitrary number they selected for the upper limit. I would guess it is to limit the amount of data the servers have to move from the disk array or something of that nature.
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What I don't understand about lost tasks is why they are only resent in batches of 20.

Because that is the arbitrary number they selected for the upper limit. I would guess it is to limit the amount of data the servers have to move from the disk array or something of that nature.

When the tasks are first sent out, there's some fairly rigorous checking done on the server (in theory, at least) to ensure that no task is sent which might possibly run into deadline trouble, given the speed of the host, what proportion of the time it's crunching, how much work it has on board from other projects, etc., etc.

I think the 'resend' logic is much simpler - which is one reason why we have this problem with VLARs. And don't forget, your computer might have gone off and collected a bucketful of work from another project in the meantime, thinking that SETI hadn't given it anything.

I think the 20 task limit is just a simple-minded precaution against overwork. You can always ask for another 20 five minutes later.

Of course I see 20 lost task resent followed by 20 Already have task
This mainly on two hosts. [Edit_ now three].
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This is an unexpected consequence from a change to the server code that was made during Tuesday's maintenance window. It will occur when you try to report more than 64 results, so it should only occur on your fastest hosts. The project has been alerted to this issue. There is more info in the thread "Unannounced Server-Side Change?"
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Another Fred
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Your machine sends a server request asking for work. The request makes it to the server, gets processed, and WUs get assigned to you. The message from the server back to you informing you of these tasks and where to download them from gets dropped due to network congestion.

Your machine will say something like "time-out window reached" after 360 seconds because it did not get a response from the server. After usually 60 seconds, it will send another scheduler request. When you send scheduler requests, it sends a copy of client_state.xml along with it which says what work you have, how long it is expected to take, etc.

The server looks at what your machine says it has, compares it to what you're supposed to have, and sends you those same tasks again, but as "lost tasks." Limited to 20 at a time, and as long as there are no crazy hardware limitations, other projects getting a whole pile of work in the meantime or you're getting too close to deadlines, you can get an indefinite number of batches of 20 resends until you have all that you're supposed to have.

The resending of lost tasks is a relatively new feature. It used to be called "ghosts" because they would show up on your tasks page here on the website, but they weren't on your machine. They would simply just sit there and wait until the deadline passed and then get sent to somebody else. The only time ghost tasks happen are when the network pipe is maxed out, which in the past 6+ months.. has been nearly 24/7.
____________Linux laptop uptime: 1484d 22h 42m
Ended due to UPS failure, found 14 hours after the fact